I have controlled multiple different types over the years, both sealed and open, but I would not attempt to control the type pictured, assuming gas lighter wood burning fireplace.

All the fireplaces that I have controlled are millivolt controlled. These all have pilot lights that heat up a thermocouple. The pilot can always be lit, or can be lit with an ignitor. The thermocouple once hot enough produces a voltage that when sent through a contact closure opens the gas valve and lights the fireplace. No pilot flame, no voltage, no gas, no fire. This is the same way that a water heater is controlled that cycles on and off unmonitored.

The problem with a wood burning fireplace is that it creates too much heat and coals that would destroy any electronics that are in place to control it.